Mathematics 2016-17—Grade 3
Weeks 30-32—April/May
enVisionmath2.0—Topic 14
Standards for Mathematical Practice
Beyond the Critical Area(s): Solving Multi-Step Problems
FOCUS for Grade 3
Supporting Work
20% of time
3.MD.B.3-4
3.G.A.1-2
Major Work
Additional Work
70% of time
10% of time
3.OA.A.1-2-3-4
3.NBT.A.1-2-3
3.OA.B.5-6
3.MD.D.8
3.OA.C.7
3.OA.D.8-9
3.NF.A.1-2-3
3.MD.A.1-2
3.MD.C.5-6-7
Fluency standards: 3.OA.C.7 and 3.NBT.A.2
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Standards in bold are specifically targeted within instructional materials.
Domains:
Measurement & Data
Clusters:
Clusters outlined in bold should drive the learning for this period of instruction.
3.MD.A Solve problems involving measurement and estimation.
Standards:
3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time
intervals in minutes, e.g., by representing the problem on a number line diagram.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply,
or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a
measurement scale) to represent the problem.
Rev 3/2017
Property of MPS
Page 1 of 8
Mathematics 2016-17—Grade 3
Weeks 30-32—April/May
enVisionmath2.0—Topic 14
Foundational Learning
2.MD.C.7
3.OA.D.8
Future Learning
4.MD.A.1-2
Key Student Understandings
 Students understand that some attributes of objects are measurable and can be quantified
using unit amounts.
 Students expand their understanding of measuring time to include measuring intervals of
time—the total amount of time that passes between a starting and ending time (elapsed
time); students also measure time to the nearest minute.
 Students understand that capacity (liquid volume) is a measure of how much liquid a
container can hold; students use this understanding to estimate and measure liquid
volumes.
 Students understand that mass is a measure of the quantity of matter in an object;
students use this understanding to estimate and measure the mass of objects.
 Students understand problems involving time, mass, and volume can be solved with using
visual representations.
Assessments

Formative Assessment Strategies

Evidence for Standards-Based Grading
Common Misconceptions/Challenges
3.MD.A Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
 When exploring elapsed time, students may not grasp that an hour of time may not look like the standard hour representation (8:00-9:00 vs 8:30-9:30 vs
2:43-3:43 all represent one hour of time).
 Avoid the use of paper plate clocks. Students need to see the actual relationship between the hour and the minute hand. This is not adequately
represented on student-made clocks.
 Students may count tick marks instead of spaces when reading a clock or using a number line. Take time to emphasize that the intervals between tick
marks are the units that are being measured.
 Students may not realize that they must fill a container measuring liquid all the way to the top in order to get an accurate measurement. Point out that
to get a valid measurement, students must fill and pour as close to the measure every time.
 Students often confuse “weight” with “mass”. Explain the difference, and model and encourage the use of “mass” when working with this content.
 Students often focus on size to determine estimates of mass. They can be confused by a big fluffy object and a tiny dense object. Because students
cannot tell actual mass until they have handled an object, it is important that teachers do not ask students to estimate the mass of objects until they have
had the opportunity to lift the objects and then make an estimate of the mass.
 Students may read the mark on a scale that is below a designated number on the scale as if it was the next number. For example, a mark that is one mark
below 80 grams may be read as 81 grams. Students realize it is one away from 80, but do not think of it as 79 grams.
Rev 3/2017
Property of MPS
Page 2 of 8
Mathematics 2016-17—Grade 3
Weeks 30-32—April/May
enVisionmath2.0—Topic 14
Instructional Practices
Domain: 3.MD
Cluster: 3.MD.A Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of
time intervals in minutes.

Students have experience in telling and writing time from analog and digital clocks to the hour and half hour in Grade 1, and to the nearest five minutes
using a.m. and p.m. in Grade 2. Grade 3 students tell and write time to the nearest minute and measure elapsed time in minutes both in and out of
context using clocks and number lines.

This standard calls for students to measure time intervals and solve for elapsed time, including word problems. Explore word problems involving addition
and subtraction of time intervals in minutes. Have students represent the problem on a number line. Students should relate to using the number line
with subtraction from Grade 2. On the number line, students should be given the opportunities to determine the intervals and size of jumps on their
number line. Students could use pre-determined number lines (intervals every 5 or 15 minutes) or open number lines (intervals determined by students).
Rev 3/2017
Property of MPS
Page 3 of 8
Mathematics 2016-17—Grade 3
Weeks 30-32—April/May
enVisionmath2.0—Topic 14

Provide analog clocks that allow students to move the minute hand. Students need experience representing time from a digital clock to an analog clock
and vice versa.
Rev 3/2017
Property of MPS
Page 4 of 8
Mathematics 2016-17—Grade 3
Weeks 30-32—April/May
enVisionmath2.0—Topic 14
3.MD.A.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract,
multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a
beaker with a measurement scale) to represent the problem.

This standard asks for students to reason about the units of mass and volume using units g, kg, and L. Students need multiple opportunities weighing
classroom objects and filling containers to help them develop a basic understanding of the size and weight of a liter, a gram, and a kilogram. Milliliters
may also be used to show amounts that are less than a liter emphasizing the relationship between smaller units to larger units in the same system. Word
problems should only be one-step and include the same units.

Foundational understandings to help with measure concepts:
o Understand that larger units can be subdivided into equivalent units (partition).
o Understand that the same unit can be repeated to determine the measure (iteration).
o Understand the relationship between the size of a unit and the number of units needed (compensatory principal).

These standards do not differentiate between weight and mass. Technically, mass is the amount of matter in an object. Weight is the force exerted on
the body by gravity. On the earth’s surface, the distinction is not important (on the moon, an object would have the same mass, would weigh less due to
the lower gravity). (Progressions for the CCSSM, Geometric Measurement, CCSS Writing Team, June 2012, page 2)

Provide opportunities for students to use appropriate tools to measure and estimate liquid volumes in liters only and masses of objects in grams and
kilograms. Students need practice in reading the scales on measuring tools since the markings may not always be in intervals of one. The scales may be
marked in intervals of two, five, ten, fifty, one hundred. This practice should be with actual measuring tools as much as possible, while also
supplementing with images like the ones pictured here:
Rev 3/2017
Property of MPS
Page 5 of 8
Mathematics 2016-17—Grade 3
Weeks 30-32—April/May
enVisionmath2.0—Topic 14

Provide students with opportunities to explore their surroundings, and find familiar objects that they can use for estimating various liquid volume and
mass measurements. Allow students to hold gram and kilogram weights in their hand to use as a benchmark. Use water with food coloring so that the
water can be seen in a beaker. Consider creating an anchor chart with student-generated benchmarks for a variety of units (see right). Examples of
some useful measurement benchmarks:
o Example: Students identify 5 things that weigh about one gram. They record
their findings with words and pictures. (Students can repeat this for 5 grams and
10 grams.) This activity helps develop gram benchmarks. One large paperclip
weighs about one gram.
Useful Benchmarks:
 An apple has a mass of about 100 grams.
 A large soda bottle holds 2 liters.
 A bottle of water holds about 1 liter.
 A grown man’s mass is about 75 kg.
 Some hardcover books have a mass of about 1 kg.

Students should be guided to think about benchmarks before making estimates. Once a
student has made an estimate, the student then measures the object and should reflect on
the accuracy of their estimate, and consider this information for the next measurement.
http://www.teachersnotebook.com/product/amgooding/metric-measuremento Example:
mini-anchor-charts-amp-benchmarks
Teacher: Look at this apple. What do you think its mass is in grams?
Student: A gram is not very much, like a paper clip. I think I could hold about a hundred paper clips to balance an apple, so I estimate an
apple’s mass is 100 grams.
Teacher: Now measure the apple and see.
Student: It is 102 grams. My estimate was really close!

Encourage students to estimate first whenever they measure (connection to MP.2). Estimation helps kids to focus on the attribute to be measured, in this
case liquid volume or mass, and the process of measuring. Show students a group containing the same kind of objects. Then, show them one of the
objects and tell them its weight. Fill a container with more objects and ask students to estimate the weight of the objects. After they find measurements,
have students discuss the estimates, their procedures for finding the measurements, and the differences between their estimates and the
measurements.

Use similar strategies with liquid measures. Be sure that students have opportunities to pour liquids into different size containers to see how much liquid
will be in different-shaped liters. Show students containers and ask, “How many liters do you think will fill the container?” If making several estimates,
students should make an estimate, then find the measurement and continue the process of estimating and then finding the actual measure, rather than
finding all estimates and then all measures. It is important to provide feedback to students on their estimates by using measurement as a way of gaining
feedback on estimates.
Rev 3/2017
Property of MPS
Page 6 of 8
Mathematics 2016-17—Grade 3
Weeks 30-32—April/May
enVisionmath2.0—Topic 14

Students are not expected to do conversions between measurement units in Grade 3; the expectation is for students to use mathematical reasoning as
they estimate and measure weight and capacity.

Much of the work involving measurement supports the work that is emphasized in third grade with multiplication:
Rev 3/2017
Property of MPS
Page 7 of 8
Mathematics 2016-17—Grade 3
Weeks 30-32—April/May
enVisionmath2.0—Topic 14
Differentiation
3.MD.A Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of
objects.
 Provide sufficient wait time to allow students to process the connection between mental benchmarks and length of
objects. Students can anchor understanding of liquid measures by estimating “more than”, ‘less than” or “about”
one liter, milliliter, etc. before measuring. Point to or hold visuals while speaking. Ask students to explain how and
why they chose a specific mental benchmark when estimating mass or liquid volume. To help all students
remember the benchmarks:
o Pair language with visuals by posting pictures of the benchmarks.
o Allow students to create a reference chart to keep track of the benchmarks as they learn them. They can
later use this chart as a reference.
 Use multiple formats for recording elapsed time: chart, number line, and bar diagrams. Use pre-printed number
lines when working with intervals of time for students with fine motor skills and/or perception limitations.
 Include different problem types (start unknown, change unknown, result unknown—see table above) for students
to solve.
Literacy Connections

Academic Vocabulary Terms

Vocabulary Strategies

Literacy Strategies
The Common Core Approach to Differentiating Instruction (engageny How to Implement a Story of Units, p. 14-20)
Linked document includes scaffolds for English Language Learners, Students with Disabilities, Below Level Students, and
Above Level Students.
Resources
enVisionmath2.0
Developing Fluency
Multiplication Fact Thinking Strategies
Topic 14 Pacing Guide
Grade 3 Games to Build Fluency
Multi-Digit Addition & Subtraction Resources
Rev 3/2017
Property of MPS
Page 8 of 8